A pediatrician is a doctor for babies, children, and teenagers — not for adults, except when the patient is still in that doctor's care. This is the American spelling. The British spelling is paediatrician, with an extra a after the p. Same doctor, same job; the letters follow American vs British habits, like pediatric / paediatric. In a hospital they work in pediatrics. Parents take a sick child to the pediatrician for checks, shots, fevers, and growing-up problems. The word is normal and respectful in American English. Though actually, you do not say 'a pediatric' for the person. That form is an adjective and wants a noun: pediatric care, a pediatric ward.